Seven Liberal Arts - Music
A presentation by Det Springende Punkt
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The Seven Liberal Arts have some of their roots in the learning traditions of the Carolignian Renaissance and the first European universities The system consists of:
- Trivium: grammar, logic & rhetoric which in time developed to the humanities
Sadly I haven't been able to come closer to the origins of the beautiful illustrations than this, sorry!
- Quadrivium: Arithmetic, Astronomy, Geometry & Music which in time developed to natural sciences
Astronomy Arithmetic
Music
Geometry
We choose to focus on music!
The noble art of music theory thus shares a root with exact sciences and has a close relation to number. Here the musical intervals are on archly display. Their sizes are indicated by the proportion number values 6 : 8 : 9 : 12. Please remember them, as part of the intention with this presentation is to give them a renaissance!
Raphael (1483-1520): School of Athens. 1509-10. Fresco. The Vatican
Raphael's mural in the pope's library is filled with ancient philosophers, many of whom have been given character by some of his well known contemporaries from Rome. Plato wearing red toga in the center of the image is depicted with the figure of Leonardo da Vinci. He is standing next to Aristotle. In the foreground Heraclitus in the figure of Michelangelo is seated by a cubic stone. But now focus on the group to the right of him!
At the time of the creation of the fresco Bramante (1444-1514) held the position of chief architect of St. Peter's Basilica. His ideas for the construction of this monumental building are reflected by the scenographic setting of the School of Athens, e.g. the barrel vault and the lacunar ceiling. It was by intervention of Bramante that Raphael came to the papal court, where he quickly rose to stardom. After Bramante's death a few years later, Raphael became chief architect of the church. Above: Euclid in Bramante's figure nails his compass to the tablet on the floor, and thus becomes representative of GEOMETRY.
In the group on the right is Raphael's friend Baldassare Castiglione in the role of Zoroaster with star sphere, and the painter has introduced a self portrait with dark beret in half profile alongside fellow artist Il Sodoma with light beret. Turning his back to the viewer Ptolemy (who was confused with an Egyptian ruler) with crown and globe is seen. Wisdom goddess Pallas Athena - with spear instead of compass - watches from her niche the right side activities. The group embodies ASTRONOMY:
In his capacity of leader of the muses Apollo is surveying left side of the picture with lyre in his hand. In the group below him at the floor, the number wizard over them all Pythagoras is making calculations in his book. ARITHMETIC
... and there is more: An angelic figure with a tablet!
The writing is in Greek and in a very condensed form displays some central Pythagorean musical concepts. Epogdoon means the proportion 8 : 9, which corresponds to a whole tone. Roman numerals are VI, VIII, VIIII & XII, ie 6 : 8 : 9 : 12. Hey, haven't we been around here before!? The other Greek interval names: Diatessaron (through four): Perfect fourth. Diapente (five): Perfect fifth. Diapason: Prime/ octave. At the bottom is depicted the Holy Tetractys: 1 + 2 +3 + 4 = 10
Translated: Within the frame of the octave, ratio 1:2 (between six and twelve), the perfect fifth and fourth, ratio 2:3 and 3:4 respectively, generate between them the whole tone interval. Expressed mathematically: 3/2 : 4/3 = 9/8. The fundamental intervals thus can be described with ratios between the first four natural numbers.
At the monochord the relevant length proportions are illustrated. Only the fundamental divisions with factors 1, 2, 3 & 4 are shown. The unit can be chosen freely. If it is 10 centimeters the full string length of the instrument would be a very realistic 120 centimeters. The intervals should be seen in the light of the string's harmonics. Thanks to Knud Brant Nielsen!
It is very understandable that so much attention has been given to the development of the visual arts during the renaissance, especially in Italy: The mysteries of perspective were solved, and Bramante played a major role here. With the School of Athens Raphael demonstrated a mastership of it matching that of Leonardo's in the Last Supper. Bramante, Leonardo, Michelangelo and Raphael were all architects. But it was definitely not all a matter of technique. That becomes obvious by contemplating the development of the use of colours and the rendering of landscapes, minerals, plants, animal and human proportion and psychology. The three dimensions were brought to live at the two dimensions of the face! Did anything nearly as significant happen in music? Groundbreaking was the development of polyphony and the harmonic cadence, which led to the majorminor tonality. It is a series of chords that make use of the natural interval tensions between the tonic, dominant and subdominant, which are based on prime, fifth and fourth respectively: 6:8:9:12 in other words ... ehr, numbers! ;-)
One of the leading musicians and theorists was Franchino Gaffurio (1451-1522), who held the position of cantor at the Milan Cathedral. Here is a woodcut from his treatise Theorica Musicae from 1492, which in its own field was as important as Columbus' discovery the same year. In addition to diapente: 2:3, fifth, and diatessaron: 3:4, fourth, the intervals in play are to and from harmonic #5: Dytonus: Just major third, 4:5 Semidytonus: Just minor third 5:6
Franchino's earlier work Theoricum Opus Musicae Disciplinae from 1480 was the first European published book about music taking advantage of Gutenberg's printing invention.
Most art historians believe that Leonardo in his only known male portrait depicted just Franchino with sheet music. Leonardo was himself a very talented musician, and it would be more appropriate to clarify what the notes say, than to spend time on the flourishing da Vinci code conjectures. Unfortunately, it is difficult to read, but it seems to be in Phrygian mode.
See, listen to and read more (so far only in Danish, sorry!) in da Vincis musikmysterium!
As in the School of Athens the music and its proportions is represented on the left side. At the lectern: A flask. 3 : 4 : 6 corresponds to 6 : 8 : 12
As in the School of Athens the geometric figures and their instrument, the compass, are represented at the right side. At the lectern: an hourglass
This woodcut shows Franchino teaching music and proportions. He has twelve tonal students, so if you count prime, halftone, whole tone, minor third, etc. from the left, the middle figure with his back to us will actually be representative of the beholder, you and me! ... and he betrays the pure harmony by incarnating the tritone, the most dissonant interval of them all! But the wise master does not have a narrow vision of the deeper aspects of harmony as he pronounces "Harmonia est Discordia concors", referring to Heraclitus (ca. 535-475 BCE) '"Opposition brings concord. Out of discord comes the fairest harmony." Just around the corner from where Franchinus worked, Leonardo was busy with his the Last Supper.
Several of the woodcuts from Teorica Musicae have been spread widely. The best known is probably the one to the left with Jubal, Philolaus and Pythagoras, who experiment with musical volumes, lengths and weights of the proportions 6 : 8 : 9 : 12. However, the myth of Pythagoras and the musical blacksmith hammers does not stand a modern sound physics analysis. Right: Plato's musical lambda figure, a musical creation matrix. See more here!
Another of the great musical masters, Josquin des Prez, was also active in Milan, and a friend of both Leonardo and Franchino. His Kyrie from Missa Pange lingua is filled with 6:8:9:12-proportions in both form, harmony, rhythm and melody. The ending anticipates the subsequent evolution of the harmonic cadence in music. Thanks to Knud!
The 6:8:9:12 of the Pythagorean tablet illustrates how the perfect fifth, 2:3, and the perfect fourth, 3:4, generate the whole tone, 8:9, within the octave frame 1:2. The pattern has a perfect symmetry. The emergence of other just interval relations - also within other frames than the octave - can be described in a similar way: 1:2:3:6 1:3:4:12 1:3:5:15 2:3:4:6 2:4:5:10 2:5:6:15 3:5:6:10 4:5:8:10 5:9:10:18 12:15:16:20 15:18:25:30 20:24:25:30 30:32:45:48
(2:3 = perfect fifth); (3:4 = perfect fourth); (3:5 = just major sixth); (3:4 = perfect fourth); (4:5 = just major third); (5:6 = just minor third); (5:6 = just minor third); (5:8 = just major sixth); (9:10 = just minor whole tone); (15:16 = just major semitone); (18:25 = tritone); (24:25 = just minor semitone); (32:45 = tritone)
The Pythagorean tablet constitutes the foundation, the 'feet' of Gaffurio's cosmological diagram based on musical intervals, with the Muses and the church modes in the role of intermediaries of the order of the planetary spheres.
... same scenario in a more poetic representation: Apollo seated with lyre (lute) in hand on his throne in the fixed stars sphere. He is 'the unmoved mover' (Aristotle / Xenophanes) and he lets the three headed serpent (past, present, and future / the three spatial dimensions) descend through the planetary spheres and the elements of the Earth. Each sphere is ruled by a muse and a church mode. At the Earth's core the muse of comedy, Thalia, has her place. Another Thalia, one of the three Graces, has her place at Apollo's side.
"Mentis Apollineae some er movet undique Musas" ~ The power of Apollo's mind move the Muses everywhere. That should be understood in the light of the Renaissance concept of 'body-soul-spirit' with - The cardinal principle, the motionless fixed stars sphere, representing the spirit; - The planetary motions representing the soul, anima; - The stagnant principle, creation, the elements, representing body.
The muses and the planetary spheres bring us back to the seven liberal arts, whose original author was Martianus Capella, a Roman from the 5th century who lived in Madaura and Carthage in the current Algeria and Tunisia respectively. In his work 'About Mercury's marriage with philology' the idea of ​the seven liberal arts represented by their muses is introduced. They are students of the precious Philology and will be her handmaidens by the wedding. The allegory had a tremendous impact on the Carolingian renaissance in the early medieval time of Europe. The adjoining reproduction of the muse of Music was published in Italy in the 15th century.
Herrad von Landsberg, ca. 1180: Septem Artes Liberales. The seven liberal arts in the circle around the wisdom, Sophia, with Plato and Socrates at her feet.